The Causal Abstraction Network: Theory and Learning
This work addresses the need for more interpretable and reliable AI systems, but it is incremental as it builds on existing formalizations of causal knowledge networks.
The paper tackled the problem of learning causal abstraction networks (CANs) to enhance AI explainability and robustness, introducing a specific instance with Gaussian structural causal models and proposing an efficient learning method that showed competitive performance on synthetic data.
Causal artificial intelligence aims to enhance explainability, trustworthiness, and robustness in AI by leveraging structural causal models (SCMs). In this pursuit, recent advances formalize network sheaves of causal knowledge. Pushing in the same direction, we introduce the causal abstraction network (CAN), a specific instance of such sheaves where (i) SCMs are Gaussian, (ii) restriction maps are transposes of constructive linear causal abstractions (CAs), and (iii) edge stalks correspond -- up to rotation -- to the node stalks of more detailed SCMs. We investigate the theoretical properties of CAN, including algebraic invariants, cohomology, consistency, global sections characterized via the Laplacian kernel, and smoothness. We then tackle the learning of consistent CANs. Our problem formulation separates into edge-specific local Riemannian problems and avoids nonconvex, costly objectives. We propose an efficient search procedure as a solution, solving the local problems with SPECTRAL, our iterative method with closed-form updates and suitable for positive definite and semidefinite covariance matrices. Experiments on synthetic data show competitive performance in the CA learning task, and successful recovery of diverse CAN structures.